A team of International Monetary Fund (IMF) experts will fly to Madrid this week. They are meant to be there for the routine annual check-up the fund carries out on all members, but it looks increasingly likely that before they leave, they will have had to draw up plans for an emergency bailout of the eurozone's fourth largest economy. This would catapult the debt crisis into a new and dangerous phase.

Bankia, which has already been rescued once by the Spanish government, announced last weekend that it needed an alarming €19bn (£15bn) to patch up its finances, battered by the Spanish property crash. This was four times what had been estimated only a fortnight earlier.

With its bank bailout fund running dangerously low, the government initially proposed filling the hole with its own bonds, which Bankia could exchange with the European Central Bank (ECB) for cash. That smacked of desperation – and strayed too close to a direct bailout of the Spanish government to be acceptable to Germany and other eurozone governments, or to the ECB itself.

Without the ECB's help, it is unclear where the cash will come from. Bankia's plight, which is far more serious than the markets had suspected, raised questions about the rest of the country's banking sector, which was once the bedrock of Spain's economy.

Yields on Spanish bonds – a proxy for the rate Madrid must pay to borrow – shot up through 6.6%, well above the level usually thought to signal an imminent budget crisis. And investors have continued to withdraw assets from Spain. Latest ECB figures show that €97bn of capital, equivalent to about 10% of Spain's GDP, was pulled out in the first three months of 2012. The yield on German bonds, however, continued to hit new lows, as nervous investors desperately sought a safe home for their cash.

Charles Wyplosz, professor of international economics at the Graduate Institute in Geneva, said: "I believe that we have reached the point of no return, where the markets have decided this is a hopeless case."

Robert Zoellick, the outgoing president of the World Bank, warned in the Financial Times on Friday that Europe might be approaching a break-the-glass moment, "when one smashes the pane protecting the emergency fire alarm".

This is a dramatic reversal. At the start of the crisis Spain's banks had been held up as a bastion of strength. In the UK, as the crisis was beginning, Santander salvaged Alliance & Leicester and was used by the Labour government to help rescue Bradford & Bingley after the collapse of Lehman Brothers.

Spanish regulators were hailed for their wisdom in preventing local banks from embarking on off-balance-sheet ventures, such as the "structured investment vehicles" that came to symbolise the 2007 credit crunch. The regulators had also forced banks to amass extra capital in the good times as a cushion against bad times – a policy the UK is now trying to emulate.

But this crisis has gone on longer than any such policy could have prepared for. Analysts at investment bank UBS reckon the Spanish banking system could need as much as €120bn of fresh capital to cope with the damage being caused not by arcane credit-crunched investments but by plain bad property lending. And because they went into the crisis stronger than other banks, when others were raising capital, Spanish banks were not.

Jonathan Loynes, chief European economist at Capital Economics, says: "The Spanish banking system looks pretty hopeless: not just Bankia… It looks as though there may be other institutions hiding losses."

Banking analysts also worry that Spain's banks are still reliant on the wholesale money markets, something UK banks are being weaned off. Their loan-to-deposit ratio – a measure of how much banks need on top of their deposits to support their lending – is 150%.

As in other troubled member states, Spain's banks and its public finances are locked together: banks' balance sheets are stuffed with their own governments' bonds. As foreign investors have avoided Spanish government bonds, the local banking sector has filled the gap.

This is potentially alarming. Loynes says: "Spain are still trying to tell us that they can muddle through on their own, but that looks very unlikely."

A Spanish crisis has always been a far more worrying prospect than the troubles of much tinier Greece, which could still spark a serious crisis. Simon Derrick, currency strategist at BNY Mellon, says: "The problem with Spain is that it's an order of magnitude larger than Greece. You're talking about the eurozone's fourth largest economy; you're talking about a very large amount of money."

A recent report from the Institute of International Finance, which represents the world's banks, suggested that on the basis of the experience of Ireland, which also saw a property bubble fuelled by reckless lending, Spain's banks could suffer losses of up to €260bn, and preventing a full-blown banking crisis could cost €60bn. Other analysts, such as those at UBS, believe the price tag could eventually be double that.

That is money that the Spanish government, already struggling to meet deficit targets set by Brussels, does not have. And the rules of the eurozone's €500bn rescue fund, the European stability mechanism (ESM), which is due to come into full operation next month, do not allow it to lend directly to financial institutions – only to governments.

Madrid is understandably reluctant to accept that it needs a bailout from the ESM. It would probably be made in concert with the IMF and, like the "rescue" of Greece, Portugal and Ireland, would come with painful conditions. A bailout would also exacerbate the already fragile mood in the markets, with investors fretting about each other's potential losses and which European country might be the next domino to fall.

Mariano Rajoy, Spain's prime minister, on Saturday proposed the creation of a new fiscal authority in the eurozone that would control and harmonise member states' national budgets and debts.

For Angela Merkel and her colleagues, seeing Spain accept a loan would be not only damaging to confidence across the eurozone, but politically painful. Unlike Greece – IMF boss Christine Lagarde told the Guardian last week that that country's plight was "payback time" for years of tax-dodging – Spain has more or less played by the rules. Rajoy is not a reckless spender, but a right-of-centre leader who has largely followed the prescription set down by his European partners for austerity and reform – at least until the grim state of the economy made it impossible to meet the deficit targets.

Merkel last week described Spain as an ally, and said Rajoy had been handed "a difficult inheritance". Optimists hope this natural political sympathy will help to soften Germany's approach to embattled eurozone countries.

The European Commission last week urged leaders to allow the ESM to act directly to rescue banks, and to form a eurozone-wide "banking union" to avoid governments with weak banking sectors being picked off by financial markets. But both these proposals would require a dramatic attitude shift in Berlin.

Mario Draghi, the president of the ECB, was clearly exasperated at German intransigence last week when he told the European parliament that leaders need to show more vision: "Can the ECB fill the vacuum of lack of action by national governments on fiscal growth? The answer is no. Can the ECB fill the vacuum of lack of action by national governments on the structural problem? The answer is no."

The Frankfurt-based bank has, by default, become the first line of defence in tackling the crisis, buying billions of euros of bonds from Italy and Spain to bring down their borrowing costs, and releasing €1tn of cut-price three-year loans to banks in December and again in February to prevent a credit crunch.

With an ECB policy meeting scheduled for Wednesday, Draghi could decide that the severity of the situation requires more emergency action, but his outburst last week suggested that he would now like to see leaders take over the situation, before it spirals out of control.

Derrick at BNY Mellon says: "He staved off a banking crisis; he bought time for the politicians to do something. The problem is, they haven't done anything with the time he bought them."

There is an EU summit planned for this month, but it looks increasingly as though leaders will have to take action before then to secure Spain's finances and demonstrate that the situation can be controlled – before it spreads to Italy, or even France, and threatens the very survival of the eurozone.